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Suppose that a sphore of diameter D moves at a velocity U relative to a liquid, and that the sphero temperature TS exceeds the liquid temperature TL far from the sphere. The rate of heat transfer from sphere to liquid (energy per unit time) may be expressed as O - hA(T s T L) where A is the surface arca of the sphere and h is the heat transfer coefficient. The value of h depends on the thermal conductivity of the liquid (k, Sl unit W m-1 K-1) and its heat capacity per unit mass at constant pressure ( , SI unit J kg-1 K-1), in addition to D, U, p, and μ. Temperature adds to (M, L, T) a fourth primary dimension, denoted as O (a) It is customary to embed h in a Nusselt number, Nu hD/k Confirm that this is dimensionless (b) If N1 - Nu, U appears only in N2, and u appears only in N3, what are suitable choices for the dimensionless groups?
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